Question

If `int_-2^3 x^2 dx = k int_0^2 x^2 dx + int_2^3 x^2 dx`, then the value of k is ______.

Options

• 2

• 1

• 0

• `1/2`

Answer 1

If `int_-2^3 x^2 dx = k int_0^2 x^2 dx + int_2^3 x^2 dx`, then the value of k is 2.

Explanation:

`int_-2^3 x^2 dx = k int_0^2 x^2 dx + int_2^3 x^2 dx`

⇒ `[x^3/3]_-2^3 = k[x^3/3]_0^2 + [x^3/3]_2^3`

⇒ `[9 + 8/3] = k[8/3] + [9 - 8/3]`

⇒ k = 2